It should be noted that KL is asymmetric in replacing \(q_1\)  and \(q_2\) . Between the two forms, many variational methods (e.g., variational Bayes) minimize the form of \(\mathrm {KL}(q \Vert \pi )\) , whereas the expectation propagation (EP) algorithm [1]} considers the divergence \(\mathrm {KL}(\pi \Vert q)\) .
See [2]} for a good discussion of the relative merits of each divergence.
